NSW Police said officers went to a home on Bulah Way in Seven Hills about 11.20am to conduct inquiries in relation to an outstanding warrant.
Police said 45-year-old Stanley Russell was shot after a “physical confrontation” broke out.
Witnesses said they heard “three to four loud bangs.”
“Many police officers around I’ve been told there is a shooting I don’t know why,” a witness said.
Acting Assistant Commissioner Julie Boon said police were approached by Mr Russell, who was armed.
“They were confronted by a 45-year-old man who was armed with a knife and an axe,” she said.
“Officers let out a series of shots and unfortunately the man collapsed.”
Officers conducted CPR until paramedics arrived, but Mr Russell could not be revived.
Ms Boon said there were four officers inside the home when the shooting took place.
“There were four officers inside the premises, I can’t yet confirm who fired the shots and how many shots were fired.”
A crime scene has been established and inquiries are underway.
A number of residential streets have been closed, with diversions in place.